1. Field of the Invention
This invention relates to nonlinear optical (NLO) devices made of single crystals of LiB.sub.3 O.sub.5.
2. Background of the Invention
a single crystal with non-zero components of the second order polarizability tensor is usually referred to as a NLO crystal. It will produce under the radiation of a laser of high intensity NLO effects such as second harmonic generation (SHG), sum-frequency generation (SFG), difference-frequency generation (DFG) and parametric amplification (OPA). The devices utilizing NLO crystals to achieve effective SHG, up and down conversion and OPA have been described in U.S. Pat. No. 3,262,058, No. 3,328,723, No. 3,747,022.
When input laser power through a NLO crystal is weak, only a small part of the incident energy will be converted into energy of different frequency. The conversion efficiency is derived as follows, EQU .eta.=Iout/Iin.alpha..vertline.Deff.vertline..sup.2 .multidot.L.sup.2 .multidot.Iin.multidot.sinc.sup.2 (K.multidot.L/2) (1)
where
Iout--output laser power PA1 Iin--input laser power, PA1 Deff--the effective SHG coefficient, PA1 L--the crystal length, PA1 .DELTA.k=k.sub.3 -(k.sub.1 +k.sub.2)--the phase mismatch. .pi./.DELTA.k is defined as the coherence length over which harmonic generation wave and incident wave can remain sufficiently in phase. PA1 d31=.-+.2.82(1.+-.0.08).times.10.sup.-9 esu. PA1 d=.+-.3.39(1.+-.0.08).times.10.sup.-9 esu. PA1 d33=.+-.0.53(1.+-.0.10).times.10.sup.-9 esu. PA1 d15=31 PA1 d24=d32
The condition that .DELTA.k=0 hence sinc (.DELTA.k L/2)=1 is called PHASE MATCHING condition. Under the condition the conversion efficiency .eta. from fundamental to harmonic generation usually arrives the maximum.
Generally phase matching is of two types:
Type I wherein the two incident waves have the same polarization;
Type II wherein the two incident waves have orthogonal polarization.
Phase matching can generally be achieved in four ways (see U.S. Pat. No. 3,949,323). We usually use the angle tuning method by rotation of the crystal to achieve it.
Two effects place restrictions on phase matching. The first is the so-called WALK-OFF effect which refers to that the phase propagation direction and energy propagation direction of the laser are different because of double refraction. The second is the phase mismatch resulting from the divergence of the incoming beam.
For a uniaxial crystal, phase matching relates exclusively to the angle .theta. which is the angle between the optical axis and the propagation direction of the incoming beam. The phase mismatch can be expressed as, ##EQU1##
Formula (2) shows that when .delta..theta. deviate from zero .DELTA.k increases and hence .theta. decreases. Generally, the deviation angle .delta..theta., at which harmonic generation power reduces to 40.5% or 1/e of the maximum, is defined as the ACCEPTANCE ANGLE. If ##EQU2## .DELTA.k does not vary linearly with .delta..theta. but rather varies with (.delta..theta.).sup.2, so that it will be insensitive to the angle deviation. This condition corresponds that .theta..sub.pm =90.degree. i.e. the propagation is in the plane perpendicular to optical axis. Phase matching under this condition is called "non-critical phase matching" (NCPM).
For a biaxial crystal phase matching relates to both .theta. and .phi. which are the polar angles of the propagation direction of the incident wave. Therefore .DELTA.k varies both with .delta..theta. and .delta..phi.. We can measure acceptance angle for .theta. with .phi. fixed and vice versa. The smaller of the acceptance angles for .theta. and .phi. is defined as the ACCEPTANCE ANGLE of a biaxial crystal. For detailed discussion of phase matching in a biaxial crystal, the paper [H. V. Hobden, J. Appl. Phys. 38(1967)4365] can be referred.
Until now the commonly used NLO crystals are KDP, Urea, KTP, KB.sub.5 O.sub.8.4H.sub.2 O et. al. Unfortunately they share the same disadvantages,
(1) No capability to generate harmonics of wavelength below 2000 .ANG., which is of great significance in the laser spectroscopy;
(2) Lower damage thresholds, that of KDP being 7 GW/cm.sup.2 when the pulse duration is 0.1 ns and the wavelength is 1.0642 .mu.m;
(3) Smaller acceptance angles, that of KDP being 5.0 mrad/cm;
These disadvantages place restrictions to use the NLO devices made of the above crystals in generating harmonics in deep UV range and with an incident laser of high energy intensity and great divergence.
The crystal structure of LiB.sub.3 O.sub.5 has been reported in [J. Anorg. Allg. Chem. (Germany) 439(1978)] and [YOGYO KYOKAISHI (Japan), 88(1980)179]. It belongs to the orthorhombic system with the space group Pna2.sub.1. The lattice parameters are respectively 8.446A, 7.378A and 5.141A for a,b,c, and Z=4 in each unit cell. The mass density is 2.478 g/cm.sup.3. The largest crystal size reported was 1.times.1.times.4 mm.sup.3, whcih was not yet large enough for practical use. And also no one has indicated that the crystals of LiB.sub.3 O.sub.5 possess NLO properties.
It is the first object of the present invention to provide a NLO device that can convert incident laser with high power density and large divergence into its harmonics with high efficiency;
The second object of the present invention is to provide a NLO device which can generate coherent radiations of wavelength below 2000 .ANG.;
It is the third object of the present invention to provide a NLO device with cross section not smaller than 70.times.70 mm.sup.2 which can be employed to generate second harmonics and third harmonics of Nd: YAG laser frequency;
The forth object of the present invention is to provide a waveguide device which can generate coherent radiation of wavelength below 2000 .ANG..
All of above objects are achieved by the NLO devices employing single crystals of LiB.sub.3 O.sub.5. Using the high temperature solution top seeding method the inventors have succeeded in obtaining single crystals of LiB.sub.3 O.sub.5 of size up to 20.times.35.times.9 mm.sup.3 which are obviously large enough for practical use.
The above NLO devices overcome some shortcomings of those employing crystals of KDP, Urea et. al. For example they can work efficiently even when the incoming beam is of high intensity (up to 25 GW/cm.sup.2 when .tau.=0.1 ns and .lambda.=1.0642 .mu.m) and large divergence (up to tens of mrad), they can also generate coherent UV radiation of wavelength below 2000 .ANG.. It is also possible to make NLO devices with LiB.sub.3 O.sub.5 crystals of large cross sections (up to 70.times.70 mm.sup.2).
The inventors have first discovered that crystals of a compound having formula LiB.sub.3 O.sub.5 possess the NLO properties. The crystals being point group of mm 2 and are therefore biaxial. They are transparent from 0.16 .mu.m to 2.6 .mu.m.
For a signle crystal of LiB.sub.3 O.sub.5 the components of d31, d32, d33, d24 and d15 of the second order polarizability tensor are non-zero. The inventors determined these components by the Maker fringer technique at the fundamental wavelength of 1.0642 .mu.m.
Employing the least deviation angle method the inventors also measured the principle refractive indices of LiB.sub.3 O.sub.5 at 16 wavelengths between 0.2537 .mu.m and 1.0642 .mu.m. By fitting procedure the Sellmeier equations were obtained. ##EQU3## where wavelength .lambda. is in .mu.m.
The inventors measured the angle tuning curves when .theta..noteq.90.degree. and .theta.=90.degree.. The acceptance angles were determined from the curves to be 25 mrad when .theta..noteq.90.degree. and 95 mrad when .theta.=90.degree..
The acceptance angle of a LiB.sub.3 O.sub.5 crystal is obviously much larger than those of KDP, Urea, KTP crystals that are commonly used in the current optcial technology. This advantage results in the smaller phase mismatch in a LiB.sub.3 O.sub.5 crystal than those in KDP, Urea, KTP et. al. under the same divergence of the laser. The large acceptance angle also make it possible to tolerate large processing error in enlargement of the cross sections of the crystals by splicing techniques. The error is only limited to a few degrees for LiB.sub.3 O.sub.5 crystal in contrast with a few minutes for KDP, of which the acceptance angle is only about 1 mrad. A SHG device with large cross sections up to 70.times.70 mm.sup.2 may be spliced using 9 piece of single crystals of LiB.sub.3 O.sub.5 of suitable size.
With a mode-locked Nd: YAG laser (.tau.=0.1 ns, .lambda.=1.0642 .mu.m) the inventors measured the threshold of a LiB.sub.3 O.sub.5 crystal to be 25 GW/cm.sup.2 which is 3.6 times as large as that of KDP under the same conditions. Therefore NLO devices made of LiB.sub.3 O.sub.5 crystals can be employed in a laser system of high power or high average power such as laser fusion system.
As the LiB.sub.3 O.sub.5 crystal is transparent from 2.6 .mu.m to 0.16 .mu.m, therefore, the NLO devices made of said crystal can achieve SHG and SFG for the incident laser, the wavelength region of which is located between 0.375 .mu.m-3.0 .mu.m.
The inventors once immersed in water at room temperature a polished single crystals of LiB.sub.3 O.sub.5 grown by the method adopted in our laboratory and observed no change of the surface brightness after one month. This shows that LiB.sub.3 O.sub.5 crystals are chemically stable and antideliquescent. Therefore NLO devices made of them can work properly without any protection.